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#include "parser.h"
#include "printer.h"
#include "polynomial.h"
#include "wallideal.h"
#include "lp.h"
#include "polyhedralcone.h"
#include "gfanapplication.h"
#include "polyhedralfan.h"
#include "halfopencone.h"
#include "linalg.h"
#include "log.h"
class GroebnerConeApplication : public GFanApplication
{
SimpleOption optionRestrict;
SimpleOption optionPair;
SimpleOption optionAsFan;
SimpleOption optionVectorInput;
public:
const char *helpText()
{
return "This program computes a Groebner cone. Three different cases are handled. The input may be a marked reduced Groebner basis in which case its Groebner cone is computed. The input may be just a marked minimal basis in which case the cone computed is not a Groebner cone in the usual sense but smaller. (These cones are described in [Fukuda, Jensen, Lauritzen, Thomas]). The third possible case is that the Groebner cone is possibly lower dimensional and given by a pair of Groebner bases as it is useful to do for tropical varieties, see option --pair. The facets of the cone can be read off in section FACETS and the equations in section IMPLIED_EQUATIONS.\n";
}
GroebnerConeApplication():
optionRestrict("--restrict","Add an inequality for each coordinate, so that the the cone is restricted to the non-negative orthant."),
optionPair("--pair","The Groebner cone is given by a pair of compatible Groebner bases. The first basis is for the initial ideal and the second for the ideal itself. See the tropical section of the manual."),
optionAsFan("--asfan","Writes the cone as a polyhedral fan with all its faces instead. In this way the extreme rays of the cone are also computed."),
optionVectorInput("--vectorinput","Compute a cone given list of inequalities rather than a Groebner cone. The input is an integer which specifies the dimension of the ambient space, a list of inequalities given as vectors and a list of equations.")
{
registerOptions();
}
const char *name()
{
return "_groebnercone";
}
int main()
{
IntegerVectorList equalities;
IntegerVectorList normals;
int n;
if(optionVectorInput.getValue())
{
FileParser P(Stdin);
n=P.parseInt();
normals=P.parseIntegerVectorList();
equalities=P.parseIntegerVectorList();
}
else
{
PolynomialSet m=FileParser(Stdin).parsePolynomialSetWithRing();
PolynomialSet g(m.getRing());
if(optionPair.getValue())
{
g=FileParser(Stdin).parsePolynomialSet(m.getRing());
}
else
{
g=m;
m=g.markedTermIdeal();
}
{
//Check that markings are consistent
PolynomialSet M1=g.markedTermIdeal();
PolynomialSet M2=m.markedTermIdeal();
assert(M1.size()==M2.size());
PolynomialSet::const_iterator i1=M1.begin();
for(PolynomialSet::const_iterator i2=M2.begin();i2!=M2.end();i1++,i2++)
{
assert((*i1-*i2).isZero());
}
}
n=g.getRing().getNumberOfVariables();
equalities=wallInequalities(m);
normals=(wallInequalities(g));
if(optionRestrict.getValue())
{
for(int i=0;i<n;i++)
normals.push_back(IntegerVector::standardVector(n,i));
}
}
{
FieldMatrix A=integerMatrixToFieldMatrix(rowsToIntegerMatrix(equalities,n),Q);
A.reduce();
A.removeZeroRows();
equalities=IntegerVectorList();
for(int i=0;i<A.getHeight();i++)
equalities.push_back(A[i].primitive());
set<IntegerVector> newInequalities;
for(IntegerVectorList::const_iterator i=normals.begin();i!=normals.end();i++)
newInequalities.insert(A.canonicalize(integerVectorToFieldVector(*i,Q)).primitive());
normals=IntegerVectorList();
for(set<IntegerVector>::const_iterator i=newInequalities.begin();i!=newInequalities.end();i++)
normals.push_back(*i);
}
log1 fprintf(Stderr,"Inequalities");
log1 AsciiPrinter(Stderr).printVectorList(normals);
log1 fprintf(Stderr,"Equations");
log1 AsciiPrinter(Stderr).printVectorList(equalities);
PolyhedralCone c(normals,equalities,n);
c.canonicalize();
if(!optionAsFan.getValue())
AsciiPrinter(Stdout).printPolyhedralCone(c);
else
{
AsciiPrinter P(Stdout);
IntegerVectorList empty;
HalfOpenCone C(n,c.getEquations(),c.getHalfSpaces(),empty,true);
// PolyhedralFan F=faceComplexOfCone(C);
PolyhedralCone C2=C.closure();
C2.canonicalize();
PolyhedralFan F(n);F.insert(C2);
F.printWithIndices(&P,FPF_default);
// F.printWithIndices(&P,false,0,false,false,optionXml.getValue());
}
return 0;
}
};
static GroebnerConeApplication theApplication;
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